Sanford also told the AP he "crossed lines" with women other than his mistress but never had sex with them, adding that he "let his guard down" with some physical contact. He said Chapur is his soul mate, but he will try to fall back in love with his wife, Jenny Sanford.

Sanford's office would not comment other than to say they will "let the AP report stand."

The governor released a statement this afternoon saying he welcomes the investigation, which will clear speculation about whether he used state money, and added that he plans to cooperate fully.

'Connection From the Very Beginning'

In what the news agency described as a long and emotional interview, Sanford, the father of four boys, said he spent two nights with the former producer in Manhattan in September 2008 and again in the Hamptons for three November days. Sanford and Chapur met again in the city this year in what was to be a farewell meeting, chaperoned by a spiritual adviser, after Sanford's wife found out about the affair in January.

The governor first met the now 41-year-old Argentinean woman -- described as "refined and professional" by her friends in Buenos Aires -- for the first time in 2001 at an open-air dance spot in Uruguay, the governor told the AP.

Sanford, who was serving his final term in Congress at the time, said the two began corresponding by e-mail after meeting on the dance floor.

"There was some kind of connection from the very beginning," he told The Associated Press, adding that he advised her that night on her failing marriage.

He then met her for a coffee date in New York in 2004 during the Republican National Convention. Sanford told the AP that neither of the first two meetings was romantic.

He continued to insist he did not use money from state coffers to finance his romantic trysts. He told the AP he flew coach for his two meetings with Chapur in New York last year, and paid for hotels in cash. Last week, he said he would reimburse the state for last year's commerce trip, but insisted he didn't do anything illegal.

When Jenny Sanford, his wife of 20 years, discovered the affair, the two went into counseling and went with a spiritual adviser to New York to break off the extramarital relationship, he said.

But Sanford flew to Buenos Aires a week and a half ago to see his mistress without telling his family, friends, security detail or staff, instead telling them he planned to go hiking on the Appalachian Trail.

Jenny Sanford said she was devastated when she found out about her husband's secret trip.

"He was told in no uncertain terms not to see her," she told The Associated Press Saturday. "I was hoping he was on the Appalachian Trail. But I was not worried about his safety. I was hoping he was doing some real soul searching somewhere and devastated to find out it was Argentina. It's tragic."

On Monday, Sanford made his second appearance after the announcement at a state budget board meeting. He apologized again to his staff for "letting you down" and said he was sorry about the affair. He also reaffirmed his decision to stay in office.

The Mystery of Maria Belen Chapur

Chapur publicly acknowledged their relationship Sunday in a statement read on Argentine TV.

Chapur remains under the radar because of intense media scrutiny surrounding her. But in a brief statement conveyed through a television report on Buenos Aires' C5N channel, she said she indeed was involved with Sanford and that the published e-mail correspondence between the two was obtained from her account by a "hacker."

The former journalist did not directly acknowledge the affair or mention the embattled governor's name, saying she won't speak about her private life, which has already been made too public and painful. But her statement offered extensive details about how "the author of this evil action" broke into her e-mail account. She denied that the hacker was a friend of hers.

Chapur's friends and colleagues told ABC News she is a sophisticated and intelligent woman, and that the relationship between the two was simply a matter of love.

Calls for Investigation

The governor, who said he initially considered resigning, is holding on firmly to his turf, saying he will complete his remaining 18 months in office in full and work to repair both his public and private relationships. Sanford told The Associated Press that he spoke with close spiritual and political associates who advised him to fight to restore the public's and his family's trust in him.

At least one member of Sanford's own party called loudly for a criminal investigation into whether the governor broke the law by not informing his lieutenant governor -- who would be in charge in case of emergency -- of his departure and using state money to finance his trips to see his mistress.

The governor's chief rival, Republican state Sen. Jake Knotts, told ABC News Sunday that he will pursue a criminal prosecution, even if he has to go to Washington, D.C.

That may not be necessary now with McMaster's call for an investigation.

McMaster, one of the frontrunners in South Carolina's gubernatorial 2010 race, is one of several who will be affected by the outcome of the Sanford scandal, analysts say.

McMaster is a leading contender for the governorship, along with Lt. Gov. Andre Bauer, who would take over the governor's seat if Sanford were to step down.

"If he [McMaster] has this investigation, he gets more publicity and name recognition if he does a good job," said Robert Oldendick, an executive director and professor at the University of South Carolina. "The downside is that if Sanford does leave office, and Lt. Gov. Bauer takes over, it gives him 15 to 16 months of incumbency leading into the race and that will be to his advantage in terms of media and name recognition."

Once the State Law Enforcement Division has completed the investigation into Sanford's travel funds, the attorney general's office will review it to see whether a criminal act has been committed and they can bring charges.

ABC News' Lisa Fletcher, John Hendren and The Associated Press contributed to this report.